U.S. patent application Ser. No. 230,384 filed on Feb. 2, 1981, in the name of K. H. Powers (now abandoned), continuation-in-part application Ser. No. 262,619 filed on May 11, 1981, (also now abandoned), continuation application Ser. No. 411,907, filed on Aug. 26, 1982, with divisional applications Ser. Nos. 411,905 and 411,906 describe linear, square-law and cubic interpolators for transcoding from television signals sampled at a first clock rate to television signals sampled at a second clock rate. These applications will be referred to hereinafter as the Powers cases. In these applications, transcoding methods and corresponding transcoders were described which utilize 2, 3 or 4 successive samples of the source signal. These applications describe simplified implementations for those transcodings in which the ratio of the clock frequencies of the two signals, i.e., F.sub.1 /F.sub.2 is equal to a fraction M/2.sup.r, where M and r are arbitrary integers. The described simplification lies in that the multiplications of the algorithm can be implemented in logic by shift registers and adders. For television signals, these applications describe the approximation of the ratio F.sub.1 /F.sub.2 by M/2.sup.r where M and r are relatively small integers. For the case of transcoding a video signal sampled at four times the NTSC standard subcarrier frequency (i.e., 4.times.SC) to a signal sampled at the CClR world-standard digital rate of 13.5 MHz, for example, the ratio is: ##EQU1## and, similarly, for the equivalent transcoding of a standard PAL signal to the 13.5 MHz standard, the corresponding ratio is: ##EQU2## It should be noted that both approximated ratios, equations 1 and 2, have the desired form M/2.sup.r, where M is either 17 (equation 1) or 21 (equation 2) and r is equal to 4.
These simplifying approximations in transcoding result in a small geometric picture distortion. For the examples given, transcoding from NTSC produces a 0.18% picture stretch and that from the PAL signal produces a 0.16% skew and 0.09% stretch. These distortions are well within the tolerance limits of camera and kinescope adjustments, and may be ignored except for those cases in which cascades of transcodings having similar distortions are encountered.
It is desirable to have alternative configurations that require a reduced number of multipliers, and to use other approximation techniques for achieving simple configurations without picture distortion.